Would you Rather: Hypothesis testing

I am teaching Type I and Type II Errors Monday and wanted to get students thinking through the problem of balancing the probability of the two errors. I want them to understand the tension and realize they will not be able to eliminate either possibility. I plan to do this before actually introducing the names for the types of errors. I just wrote up these two “Would you rather?” scenarios. I would love some feedback or some other suggestions to use as follow up.

For the two scenarios below, decide which error would be worse. Clearly state your answer and your reasoning.

Scenario 1

As a doctor, you see a large national study that 35.9% of Americans are now considered obese (H_0:p=.359). Alternatively, you think it may be possible that your patients are below the national average (H_a:p<.359). If you conduct a hypothesis test on a sample of your patients, which would be worse?

a.Rejecting the null hypothesis and stating that less than 35.9% of your patients are obese when in fact your patients are in line with the national average.
b. Failing to reject the null hypothesis that your patients match the national average, when in fact less than 35.9% of your patients are obese?

Scenario 2

You are a researcher. Patients using the current treatment for lung cancer go into remission 55% of the time (H_0:p=.55). You believe that you have found an improved treatment (H_a:p>.55). Which would be worse?

a. Rejecting the null hypothesis and stating that your treatment is better when in fact it is not.
b. Failing to reject the null hypothesis that your treatment is equal to the current treatment, when in fact it is better.

4 thoughts on “Would you Rather: Hypothesis testing

  1. Good scenarios. There is a worksheet I use for errors, created by a retired teacher near my school outisde Philadelphia. He provides scenarios like “If I cheat, I might get caught”, “Saddam Hussein has weapons of mass destruction” and “heaven and hell exists”, which are great for conversation.

    While I often hold debates as to which would be better or worse, maybe this should be thought more of as a continuum. Place type 1 error on one side, type 2 on the other, and slide towards the one you would like to minimize. This is more like what is done in practice, where we can’t eliminate error, but can try to minimize one at the risk of the other.

    • Bob, thanks for the feedback! I would love to see that worksheet if you have it available. I like the idea of a slider. I have the TI Navigator system and I wonder if it would let me send out poll questions in a similar format.

      • You should be able to send out quick polls via the navigator system. The one quirk is that students will need to be able to log in, or at least make sure the calc is online. Its really not that difficult, though I dont use it as much as id like.

        Id love to see that worksheet as well, Bob.

        • Scott, I did look into it. My students and I are pretty familiar with quick polling. I use it frequently enough. I just couldn’t remember if there was a slider option. There wasn’t, but it could be done using a multiple choice option with a scale from strongly agree to strongly disagree, or something like that.

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